investigation of shear stud performance in flat plate

Title of Paper (14 pt Bold, Times, Title case)J. Eng. Technol. Sci., Vol. 46, No. 3, 2014, 328-341
Received May 17th, 2013, 1st Revision January 30th 2014, 2nd Revision April 1st, 2014, 3rd Revision May 7th,
2014, Accepted for publication June 25th, 2014. Copyright © 2014 Published by ITB Journal Publisher, ISSN: 2337-5779, DOI: 10.5614/j.eng.technol.sci.2014.46.3.7
Investigation of Shear Stud Performance in Flat Plate
Using Finite Element Analysis
2 & A.S. Santhi
Chennai 600066, Tamil Nadu, India 2
VIT University, Vellore 632007, Tamil Nadu, India email: [email protected]
Abstract. Three types of shear stud arrangement, respectively featuring an
orthogonal, a radial and a critical perimeter pattern, were evaluated numerically.
A numerical investigation was conducted using the finite element software
ABAQUS to evaluate their ability to resist punching shear in a flat plate. The
finite element analysis here is an application of the nonlinear analysis of
reinforced concrete structures using three-dimensional solid finite elements. The
nonlinear characteristics of concrete were achieved by employing the concrete
damaged plasticity model in the finite element program. Transverse shear stress
was evaluated using finite element analysis in terms of shear stress distribution
for flat plate with and without shear stud reinforcement. The model predicted
that shear studs placed along the critical perimeter are more effective compared
to orthogonal and radial patterns.
Keywords: flat plate; ABAQUS; shear reinforcement; punching shear strength; slab
column connection; concrete damaged plasticity.
1 Introduction
A flat-plate system consists of reinforced concrete slabs of uniform thickness,
without beams, drops or column capitals, which transfer loads directly to
supporting columns. The main advantages of this system are reduced storey
height and simple formwork, leading to fast construction and further reduction
of material costs. Architecturally, the location of the columns and walls is not
restricted by the location of any beams. Flat plate can be constructed as thin as
125 mm [1]. For these reasons, flat plate is widely used for multi-story
structures. However, in flat-plate structures, the slab-column connection is
subjected to a combination of high bending moments and high shear stresses,
which can lead to brittle punching shear failure at a load that is well below its
flexural strength. Punching shear capacity is influenced by thickness of slab,
flexural reinforcement, grade of concrete, size of column, etc. Most building
codes mention that provision of shear reinforcement will increase the punching
shear capacity of the slab-column connection. The performance of many types
of shear reinforcement, including vertical and inclined stirrups, shear studs,
Investigation of Shear Stud Performance in Flat Plate 329
bent-up bars, hooked bars, and welded wire fabrics, has been tested extensively
in the last few decades. Among these, shear studs show the best performance in
both punching shear resistance and ductility [2]. The critical section for
punching shear is at a distance of d/2 (d = effective depth) from the face of the
column. When the shear stress at the critical section exceeds the design value,
shear reinforcement should be provided. Shear stresses should be investigated at
successive sections from the support and shear reinforcement should be
provided up to a section where shear stress does not exceed the allowable shear
strength of the concrete.
The finite element method is a numerical technique widely used in the
engineering field. With the advancement of the understanding of the material
properties of concrete, various constitutive laws and failure criteria have been
developed to model the behavior of concrete. Therefore, an increasing number
of researchers are using finite element analysis to study the response of
reinforced concrete structures. Finite element modeling of a flat-plate system
requires that the punching shear failure of the slab column connections is
reproduced properly. Such a simulation has been the focus of many numerical
studies using various elements.
ABAQUS is a well-established commercial finite element code. Its constitutive
models treat concrete as a continuous isotropic linearly elastic-plastic strain-
hardening fracture material. The software provides the capability of simulating
damage using three crack models for reinforced concrete elements: (i) the
smeared crack concrete model; (ii) the brittle crack concrete model; and (iii) the
concrete damaged plasticity model. Out of these three models, the concrete
damaged plasticity model was selected for the present study because this
technique has the potential to represent complete inelastic behavior of concrete
both in tension and in compression, including damaged characteristics. The
concrete damaged plasticity model assumes that the two main failure
mechanisms in concrete are tensile cracking and compression crushing.
2 Research Significance
Eurocode 2 and ACI codes recommend the arrangement of shear studs around
the slab-column connection in orthogonal and radial patterns. In an orthogonal
pattern, shear studs are placed parallel to the column edges, which will arrest
crack propagation in the orthogonal direction. In a radial pattern, shear studs are
arranged along radial lines. This will arrest crack propagation in the radial
direction. A critical perimeter pattern is a combination of orthogonal and radial
patterns that can arrest crack propagation in both directions. According to ACI
421.1R [3], the gap between two shear stud lines should not exceed a distance
of 2d, which can be maintained with a critical perimeter pattern but is not
330 Viswanathan,et al.
feasible with the other two patterns. This paper examines the effectiveness of
orthogonal, radial and critical perimeter patterns as shown in Figure 1.
(a) Orthogonal pattern (b) Radial pattern (c) Critical perimeter pattern
Figure 1 Arrangement of shear studs.
3 Finite Element Model
In order to incorporate the nonlinear behavior of the concrete, the concrete
damaged plasticity model in ABAQUS was used. This provides a general
capability for modeling concrete and other quasi-brittle materials in all types of
structures (beams, trusses, shells, and solids). This model uses the concepts of
isotropic damaged elasticity in combination with isotropic tensile and
compressive plasticity to represent the inelastic behavior of concrete. This
model is designed for applications in which the concrete is subjected to arbitrary
loading conditions, including cyclic loading. The model takes into consideration
the degradation of elastic stiffness induced by plastic straining both in tension
Figure 2 Response of concrete to uniaxial loading in tension.
0.50d
0.75d
d
and compression. It also accounts for stiffness recovery effects under cyclic
loading. The model is a continuum, plasticity-based damage model for concrete.
It assumes that the main two failure mechanisms are tensile cracking and
compressive crushing of the concrete material. The evolution of the yield (or
failure) surface is controlled by two hardening variables linked to failure
mechanisms under tension and compression loading. The response of concrete
to uniaxial loading, both in tension and compression, are shown in Figures 2
and 3 (ABAQUS manual). Input parameters required for this model are
plasticity, compression and tension, which are described below.
Figure 3 Response of concrete to uniaxial loading in compression.
3.1 Plasticity Parameters
There are five parameters that need to be defined to solve the Drucker-Prager
plastic flow function and the yield function proposed by Lubliner, et al. [4]. To
obtain exact values of the various parameters for the concrete damaged
plasticity model, a uniaxial compression test, a uniaxial tension test, a biaxial
failure in plane state of stress and triaxial test would have to be carried out for
the material, but due to the lack of sufficient information, the default parameters
in ABAQUS and the parameters proposed in other publications have been used.
The parameters needed to describe the plastic properties of concrete are:
3.1.1 Dilation Angle ψ
The ratio of volume change to shear strain is called the dilation angle. In the
Drucker-Prager formulation, the value of the dilation angle is to be determined
for the element under biaxial compression at high confining pressures.
According to Vermeer and de Borst [5], the typical dilation angle for concrete is
12° and this value was used in this model.
3.1.2 Eccentricity
This parameter is the rate at which the Drucker-Prager function approaches the
asymptote. With an eccentricity tending to zero the plastic flow tends to a
straight line. In further calculations, an eccentricity of 0.1 was used. This value
is used to get a soft curvature of the potential flow and provides almost the same
dilation angle for a wide range of confining pressure values.
3.1.3 σco/σbo Parameter
This is the ratio of the initial equibiaxial compressive strength to the uniaxial
compressive strength. This parameter is necessary to solve the yield function.
The default value 1.16 was used in this model.
3.1.4 Viscosity Parameter
The viscosity parameter is required when a convergence problem is caused by
softening behavior. As flat-plate models cause convergence difficulties, the
viscosity parameter was assumed to be 0.05.
3.1.5 KcParameter
The value of the Kc parameter is to be determined considering the yield surface
in the deviatory plane, as shown in Figure 4 (ABAQUS manual). Kc is the ratio
of the second stress invariant on the tensile stress meridian (T.M.) to the second
stress invariant on the compressive stress meridian (C.M.). The value 2/3 was
used in the calculations.
3.1.6 Compressive Behavior
An accurate model of the compressive behavior is necessary for this analysis.
Values of ultimate strength, yield strength and compression damage were taken
from the ABAQUS verification manual, which assumes that the yield strength
is 74% of the ultimate strength and the plastic strain at failure is 0.12%
3.1.7 Tensile Behavior
The concrete damaged plasticity modelallows determination of post failure
behavior in tension by defining strain, crack opening or fracture energy towards
plastic tensile stress. These three options are related to one another and the
choice of them depends on the knowledge of structural behavior and material.
The input values required for tensile behavior were taken from the ABAQUS
verification manual [6].
To analyze the effectiveness of different shear stud arrangements, four flat-plate
slabs were modeled. Slab 1 was modeled without shear studs; slab 2 was
(a) Slab 1 (b) Slab 2
(c) Slab 3 (d) Slab 4
Figure 5 Slab models.
modeled with shear studs in an orthogonal pattern; slab 3 was modeled with the
studs in a radial pattern, and in slab 4 the studs were placed in a critical
perimeter pattern as a matrix grid, as shown in Figure 5. The size, shape and
elements of the flat-plate model selected for this study are similar to the ones
used by H. Marzouk, et al. [2]. Slabs with a size of 1500 mm x 1500 mm x 125
mm were modeled with 4107 eight node linear hexahedral elements (C3D8R)
(Figure 6). Each element has eight corner nodes, and each node has three
degrees of freedom (translation in the X, Y and Z direction). The concrete is
assumed to be homogeneous and isotropic.
Figure 6 Finite Element Model of slab.
The slab is simply supported along the four sides and load is applied at a
column stub area of 200 mm x 200 mm (Figure 7). To avoid movement and
rotation of the plane, two opposite corners are fixed [7]. The column stub is
represented as a uniform load applied over an area 200 mm x 200 mm
equivalent to the area of the stub, as is generally used in this kind of slab
analysis.
Figure 7 Flat-plate model.
Since the punching failure of the slab is being studied and not the joint stiffness
as a whole, the assumption made is a reasonable one. Thus, the situation of
stress concentration in the corner area, which causes difficulties in concrete
modeling, is avoided. There are 7 and 6 pieces of 8 mm bar at the bottom and
top respectively in both directions. Flexural reinforcement was modeled with 20
linear truss elements (T3D2) and provided as per direct design method.
Interaction between the concrete and the reinforcing steel was achieved by
using an interaction module in which reinforcement is implemented as elements
embedded in the concrete’s host elements. Therefore, the assumed ideal
bonding behavior between the concrete and the reinforcing steel has to be taken
into account. A shear stud was modeled with 1308 four node tetrahedral
elements (C3D4) (Figure 8)with an 8 mm diameter stem and a 24 mm head
diameter, similar to the one used by Carl EriksBroms [8]. There are 24 pieces
Figure 8 Finite element model of shear stud.
Table 1 Compressive Stress-Strain values for Concrete.
Sl.
No.
Stress
1 24.00 0.0000 0.000
2 29.20 0.0004 0.129
3 31.70 0.0008 0.242
4 32.30 0.0012 0.341
5 31.76 0.0016 0.426
6 30.37 0.0020 0.501
7 28.50 0.0024 0.566
8 21.90 0.0036 0.714
9 14.89 0.0050 0.824
10 2.95 0.0100 0.969
of shear studs provided at a distance of d/2 from the face of the column and at
an interval of 0.75d for all three slabs. Many trials were carried out for mesh
convergence to obtain reliable results with a finer mesh. The software evaluates
all shear and normal stresses at each node, out of which shear stress S12 is
considered in the comparison. Suitable material properties, compressive and
tensile stress-strain behavior of concrete from the ABAQUS verification manual
were used in this model (Table 1-3).
Table 2 Tensile Stress-Strain Values for Concrete.
Sl.
No.
Stress
5 Comparison between FEM Results and Code Predictions
The FEM results of the punching shear strength were compared with the
predictions based on the equations specified in ACI-318M-08 [9], CEB-FIP MC
90 [10] and Eurocode 2 [11].
ACI 318M-08 has the expression for the nominal shear strength of concrete
given by
where√ should not exceed 8.3Mpa.
The variable b is the perimeter of the critical section located at a distance of
0.5d from the faces of the column.
The Eurocode 2 provisions are effectively identical to those of CEB-FIP MC 90
with the expression of the nominal shear strength of concrete given by
[ √
]
where and the term 200/d should not exceed 1.
The characteristic concrete cylinder strength is limited to 50MPa and ρ
(flexural reinforcement ratio), calculated as √ , is limited to a
maximum of 0.02.
(MC 90, s < 0.75d) (3)
( -
)
whereα is angle between shear reinforcement and plane of slab.
if 0.5d < s1.5d (ACI 421.1R) (6)
[ √
]
( ) (ACI 421.1R), (8)
whereu is the perimeter of the outer most peripheral line ofthe shear
reinforcement.
The FEM results are compared with the predictions according to ACI421.1R-99
and CEB-FIP Model Code1990 in Table 4.
Table 4 FEM results versus code predictions.
S. No. Specimen Slab2 Slab3 Slab4
Code
ACI
2 Vn1,kN 352 386 352 386 352 386
3 Vn1,max,kN 271 473 271 473 271 473
4 Vn2,kN 192 235 166 212 168 214
5 Vpred,kN 271 386 271 386 271 386
6 VFEM,kN 255 276 281
7 VFEM,/ Vpred 0.94 0.66 1.01 0.72 1.03 0.73
The investigation of transverse shear stress around the slab-column connection
has been carried out using finite element analysis because it is difficult to obtain
this distribution and its associated parameters from experimental investigation.
Results obtained from this model are reliable for three reasons: (i) the load-
deflection response of the flat-plate system (Figure 9) obtained from this model
is similar to the one obtained by many experimental investigations by other
researchers; (ii) the high shear-stress concentration in the top surface of the slab
near the loading face (0.5d to 2d) matches with the critical section for shear
mentioned by various building codes (Figure 10); and (iii) the truncated cone
visualized in the plastic strain result of this model (Figure 11) resembles the
formation of the punching cone caused by the diagonal cracking around the
column.
Figure 11 Crack pattern of punching shear failure.
In slab 1, a node that attained the maximum shear stress value was identified,
along which seven nodes were selected from the face of the column to a
distance of 2d. At these selected nodes, shear stress distribution in slab 1, slab 2,
slab 3, and slab 4 was determined at an ultimate load of 228kN, 255kN, 276kN
and 281kN, respectively. From the graph (Figure 12) it is very clear that the
shear stress value of the concrete for the slab with shear studs at most of the
nodes was well below that of the slab without shear studs. Slab 3 and slab 4
showed very good performance against punching shear strength compared to
slab 2.
Figure 12 Shear stress distribution of concrete.
A comparison of maximum punching shear strength, ultimate shear stress, and
maximum central deflection of all four slabs is shown in Table 5. The enhanced
behavior observed in the critical perimeter pattern can be due to the fact that all
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
S h
without shear stud
studs are arranged in two rows that are within 1.5d distance from the column
face, whereas in the orthogonal and radial patterns, the studs are in three rows
that are at a distance of up to 2d.
Table 5 Finite Element Analysis Results.
Specimen Shear
Slab 2 Orthogonal
Slab 4 Critical perimeter
pattern 5.95 281 79.4
7 Conclusions
In this paper, a nonlinear analysis of flat-plate systems with three different shear
stud arrangements was performed using the ABAQUS software program. Based
on the numerical results, it can be concluded that away from the face of the
column, shear stress reduces gradually. The punching shear strength is higher
for the critical perimeter pattern than for the other patterns. The critical
perimeter pattern and radial pattern show improved ductility characteristics
compared to the orthogonal pattern. This model agrees well with ACI prediction
compared to CEB-FIP MC 90 prediction.
Nomenclature
AV = Total area of shear reinforcement on peripheral line around
column C = Width of circular column
D = Effective depth of slab
dc = Compression damage factor
E0 = Initial elastic stiffness
S = Spacing of stirrup
Vc = Nominal punching capacity of concrete without shear
reinforcement Vpred = Predicted shear strength of slab; maximum of {[minimum of
Row2 and Row3] and Row 4} of Table 4 VFEM = Shear strength determined using finite element analysis
Vn1 = Nominal punching capacity with shear reinforcement
Vn1,max = Upper bound for punching capacity
Vn2 = Nominal shear strength outside shear reinforcement zone
= Equivalent plastic strain in tension
= Equivalent plastic strain in compression
dt = Tension damage factor
Ρ = Flexural reinforcement ratio
References
[1] Plain and Reinforced Concrete-Code of Practice, IS 456:2000, Bureau of
Indian Standards, New Delhi, India, 2000.
[2] Marzouk, H. & Jiang, D., Finite Element Evaluation of Shear
Enhancement of High Strength Concrete Plate, ACI Structural Journal,
93, pp. 667-673, 1996.
(ACI421.1R-99), American Concrete Institute, Farmington Hills,
Michigan, USA, 1999.
[4] Lubliner, J., Oliver, J., Oller, S. & Onate, E., A Plastic-Damage Model
for Concrete, International Journal of Solids and Structures, 25(3), pp.
229-326, 1989.
[5] Vermeer, P.A. & de Borst, R., Non-Associated for Soils, Concrete and
Rock, Delft University of Technology, Heron, 1984.
[6] ABAQUS Manual, Example Problems, Verification Manual (Version
6.5), Dassault Systèmes Simulia Corp., Providence, RI, USA, 2005.
[7] Xiao, R.Y. & Flaherty., T.O., Finite-Element Analysis of Tested Concrete
Connections, Computers and Structures, 78, pp. 247-255, 2000.
[8] Broms, C.E., Ductility of Flat Plates: Comparison of Shear
Reinforcement Systems, ACI Structural Journal, 104(6), pp. 703-711,
2007.
Concrete (ACI 318M-05) and Commentary, American Concrete Institute,
Farmington Hills, Michigan, USA, 2005.
[10] Joint CEB-FIP Committee, Model Code 90, CEB Bulletin, No. 213-214,
Lausanne, Switzerland, pp. 437, 1993.
[11] Eurocode 2, Design of Concrete Structures, Part 1-1: General Rules and
Rules for Buildings, European Standards, CEN, EN1992-1-1, Brussels,
Belgium, pp. 225, 2004.

investigation of shear stud performance in flat plate

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